We present a neural network for the solution of the inverse swarm problem of deriving cross sections from swarm transport data. To account for the uncertainty inherent to this somewhat ill-posed inverse problem, we train the neural network using cross sections from the LXCat project, paired with associated transport coefficients found by the numerical solution of Boltzmann’s equation. The use of experimentally measured and theoretically calculated cross sections for training encourages the network to avoid unphysical solutions, such as those containing spurious energy-dependent oscillations. We successfully apply this machine learning approach to simulated swarm data for electron transport in helium, separately determining its elastic momentum transfer and ionisation cross sections to within an accuracy of 4% over the range of energies considered. Our attempt to extend our method to argon was less successful, although the reason for that observation is well-understood. Finally, we explore the feasibility of simultaneously determining cross sections of helium using this approach. We have some success here, determining elastic, total n = 2 excitation and ionisation cross sections to 10%, 20% and 25% accuracy, respectively. We are unsuccessful in properly unfolding the separate n = 2 singlet and triplet excitation cross sections of helium, but this is as expected given their similar threshold energies.

The pulsed-Townsend (PT) experiment is a well known swarm technique used to measure transport properties from a current in an external circuit, the analysis of which is based on the governing equation of continuity. In this paper, the Brambring representation (1964 Z. Phys. 179 532) of the equation of continuity often used to analyse the PT experiment, is shown to be fundamentally flawed when non-conservative processes are operative. The Brambring representation of the continuity equation is not derivable from Boltzmann’s equation and consequently transport properties defined within the framework are not clearly representable in terms of the phase-space distribution function. We present a re-analysis of the PT experiment in terms of the standard diffusion equation which has firm kinetic theory foundations, furnishing an expression for the current measured by the PT experiment in terms of the universal bulk transport coefficients (net ionisation rate, bulk drift velocity and bulk longitudinal diffusion coefficient). Furthermore, a relationship between the transport properties previously extracted from the PT experiment using the Brambring representation, and the universal bulk transport coefficients is presented. The validity of the relationship is tested for two gases Ar and SF₆, highlighting also estimates of the differences.

Seminal gas discharge experiments of the late 19th and early 20th centuries laid the foundations of modern physics, and the influence of this “golden era” continues to resonate well into the 21st century through modern technologies, medical applications, and fundamental scientific investigations. Key to this continuing success story has been the kinetic equation formulated by Ludwig Boltzmann in 1872, which provides the theoretical foundations necessary for analyzing such highly non-equilibrium situations. However, as discussed here, the full potential of Boltzmann’s equation has been realized only in the past 50 years or so, with modern computing power and analytical techniques facilitating accurate solutions for various types of charged particles (ions, electrons, positrons, and muons) in gases. Our example of thermalization of electrons in xenon gas highlights the need for such accurate methods—the traditional Lorentz approximation is shown to be hopelessly inadequate. We then discuss the emerging role of Boltzmann’s equation in determining cross sections by inverting measured swarm experiment transport coefficient data using machine learning with artificial neural networks.

Electron scattering cross sections for pyridine in the energy range 0–100 eV, which we previously measured or calculated, have been critically compiled and complemented here with new measurements of electron energy loss spectra and double differential ionization cross sections. Experimental techniques employed in this study include a linear transmission apparatus and a reaction microscope system. To fulfill the transport model requirements, theoretical data have been recalculated within our independent atom model with screening corrected additivity rule and interference effects (IAM-SCAR) method for energies above 10 eV. In addition, results from the R-matrix and Schwinger multichannel with pseudopotential methods, for energies below 15 eV and 20 eV, respectively, are presented here. The reliability of this complete data set has been evaluated by comparing the simulated energy distribution of electrons transmitted through pyridine, with that observed in an electron-gas transmission experiment under magnetic confinement conditions. In addition, our representation of the angular distribution of the inelastically scattered electrons is discussed on the basis of the present double differential cross section experimental results.

We report results from the application of our optical potential and relativistic optical potential methods to electron–zinc scattering. The energy range of this study was 0.01–5000 eV, with original results for the summed discrete electronic-state integral excitation cross sections and total ionization cross sections being presented here. When combined with our earlier elastic scattering data [Marinković et al., Phys. Rev. A 99, 062702 (2019)], and the quite limited experimental and theoretical results for those processes from other groups, we critically assemble a recommended integral cross section database for electron–zinc scattering. Electron transport coefficients are subsequently calculated for reduced electric fields ranging from 0.1 to 1000 Td, using a multiterm solution of Boltzmann’s equation. Some differences with corresponding results from the earlier study of White et al. [J. Phys. D: Appl. Phys. 37, 3185 (2004)] were noted, indicating in part the necessity of having accurate and complete cross section data, over a wide energy regime, when undertaking such transport simulations.